I am running a Mac and have today started to have issues opening Indesign CC, it opens but as soon as I starts to load the screen where it offers you the files (new or existing) it crashes.
I have created a new admin user which solves the issue but I want to fix my normal user instead of moving stuff between users which is a pain.
There is apparently corruption in your current user because creating a new user solves the problem.
The only alternative I know of to use the current user is to back up everything, and do a clean install of your operating system, then carefully add back files from your backup.
It might be as simple as trashing the prefs (see Replace Your Preferences), but if that doesn't work, deleting the entire InDesign folder from each of the two locations in your user library and replacing them with copies from the working user will probably do the trick.